In this paper we present the exact solution of the Riemann Problem for the non-linear shallow water equations with a step-like bottom. The solution has been obtained by solving an enlarged system obtained by adding an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step. The resulting solution is unique and satis es the p...

Unsteady interfacial problems, considered in an Eulerian form, are studied. The phenomena are modeled using the incompressible viscous Navier–Stokes equations to get the velocity field and an advection equation to predict interface evolutions. The momentum equation is solved by means of an implicit hybrid augmented Lagrangian–Projection method, whereas an explicit characteristic method coupled ...

0021-9991/$ see front matter 2012 Elsevier Inc http://dx.doi.org/10.1016/j.jcp.2012.06.035 ⇑ Corresponding author. Tel.: +39 3277706003. E-mail addresses: [email protected] (D. Ka The set of 3D inviscid primitive equations for the atmosphere is dimensionally reduced by a Discontinuous Galerkin discretization in one horizontal direction. The resulting model is a 2D system of balance laws wi...

A new numerical code, called SFUMATO, for solving self-gravitational magnetohydrodynamics (MHD) problems using adaptive mesh refinement (AMR) is presented. A block-structured grid is adopted as the grid of the AMR hierarchy. The total variation diminishing (TVD) cell-centered scheme is adopted as the MHD solver, with hyperbolic cleaning of divergence error of the magnetic field also implemented...

Amacroscopic two-fluid model of compressible particle-laden gas flows is considered. The governing equations are discretized by a high-resolution finite element method based on algebraic flux correction. A multidimensional limiter of TVD type is employed to constrain the local characteristic variables for the continuous gas phase and conservative fluxes for a suspension of solid particles. Spec...

Received 9/8/2002; accepted 10/1/2002. For correspondence or reprints contact: Nan-Jing Peng, M.D., Department of Nuclear Medicine, Kaohsiung Veterans General Hospital. 386 Ta-Chung 1st Road, Kaohsiung 813, Taiwan, ROC. Tel: (886)7-3422121 ext. 6418, Fax: (886)7-3461179, E-mail: [email protected] Background: The scintigraphic findings of triple-vessel coronary artery disease (TVD) may va...

In this paper we review the algorithm development and applications in high resolution shock capturing methods, level set methods and PDE based methods in computer vision and image processing. The emphasis is on Stanley Osher's contribution in these areas and the impact of his work. We will start with shock capturing methods and will review the Engquist-Osher scheme, TVD schemes, entropy conditi...

This work addresses a theory of convergence for finite volume methods applied to linear equations. A non-consistent model problem posed in an abstract Banach space is proved to be convergent. Then various examples show that the functional framework is non-empty. Convergence with a rate h 1 2 of all TVD schemes for linear advection in 1D is an application of the general result. Using duality tec...

• This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into lowdensity stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibr...